24.14 Replicate and rotate

Function: %xsubvector from to vec start past

Macro: xsubvector V from to

Extended subvector procedure replicating the selected subvector “up and down” index space, in both the positive and negative directions.

The call:

(%xsubvector from to '#(#\a #\b #\c #\d #\e #\f #\g) 3 6)

selects the subvector #(#\d #\e #\f) and defines the conceptual bidirectionally–infinite vector:

...  e  f  d  e  f  d  e  f  d  e  f ...
... -5 -4 -3 -2 -1  0 +1 +2 +3 +4 +5 ...
                    ^

that is #(#\d #\e #\f) repeated in both directions. %xsubvector returns the subvector of this vector beginning at index from, and ending at to.

We can use this function to perform a variety of tasks:

• To replicate a vector:

  (xsubvector '#(#\a #\b #\c) 0 7)
  ⇒ #(#\a #\b #\c #\a #\b #\c #\a)
  

• To rotate a vector left:

  (xsubvector '#(#\a #\b #\c #\d #\e #\f) 1  7)
  ⇒ #(#\b #\c #\d #\e #\f #\a)
  
  (xsubvector '#(#\a #\b #\c #\d #\e #\f) 2  8)
  ⇒ #(#\c #\d #\e #\f #\a #\b)
  
  (xsubvector '#(#\a #\b #\c #\d #\e #\f) 3  9)
  ⇒ #(#\d #\e #\f #\a #\b #\c)
  
  (xsubvector '#(#\a #\b #\c #\d #\e #\f) 4 10)
  ⇒ #(#\e #\f #\a #\b #\c #\d)
  
  (xsubvector '#(#\a #\b #\c #\d #\e #\f) 5 11)
  ⇒ #(#\f #\a #\b #\c #\d #\e)
  

• To rotate a vector right:

  (xsubvector '#(#\a #\b #\c #\d #\e #\f) -1 5)
  ⇒ #(#\f #\a #\b #\c #\d #\e)
  
  (xsubvector '#(#\a #\b #\c #\d #\e #\f) -2 4)
  ⇒ #(#\e #\f #\a #\b #\c #\d)
  
  (xsubvector '#(#\a #\b #\c #\d #\e #\f) -3 3)
  ⇒ #(#\d #\e #\f #\a #\b #\c)
  
  (xsubvector '#(#\a #\b #\c #\d #\e #\f) -4 2)
  ⇒ #(#\c #\d #\e #\f #\a #\b)
  
  (xsubvector '#(#\a #\b #\c #\d #\e #\f) -5 1)
  ⇒ #(#\b #\c #\d #\e #\f #\a)
  

Note that:

• The from/to indices give a half–open range; the items from index from up to, but not including, index to.
• The from/to indices are not in terms of the index space for vector vec. They are in terms of the replicated index space of the subvector defined by vec, start, and past.

It is an error if start equals past.

Function: xvector-xcopy! from to target target-start source source-start source-past

Macro: vector-xcopy! target-S source-S from to

Exactly the same as %xsubvector, but the extracted text is written into the selected subvector of target.

This operation is not defined if (eq? target start); we cannot copy a vector on top of itself.